Vector

A collection of essential vector operations that provide foundational functionality for numerical computation, machine learning, and data analysis. These operations include distance measurements, similarity coefficients, and other basic and complex operations related to vectors. Through understanding and implementing these functions, we can perform a wide variety of tasks ranging from data processing to advanced statistical analyses.

vector::add

The vector::add function performs element-wise addition of two vectors, where each element in the first vector is added to the corresponding element in the second vector.

vector::add(array, $other: array) -> array

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "[2, 4, 6]"

*/

RETURN vector::add([1, 2, 3], [1, 2, 3]);

-- [2, 4, 6]

vector::angle

The vector::angle function computes the angle between two vectors, providing a measure of the orientation difference between them.

vector::angle(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "0.36774908225917935f"

*/

RETURN vector::angle([5, 10, 15], [10, 5, 20]);

-- 0.36774908225917935f

vector::cross

The vector::cross function computes the cross product of two vectors, which results in a vector that is orthogonal (perpendicular) to the plane containing the original vectors.

vector::cross(array, $other: array) -> array

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "[-3, 6, -3]"

[[test.results]]
value = "[-3, 6, -3]"

*/

RETURN vector::cross([1, 2, 3], [4, 5, 6]);

[-3, 6, -3]

vector::divide

The vector::divide function performs element-wise division between two vectors, where each element in the first vector is divided by the corresponding element in the second vector.

vector::divide(array, $other: array) -> array

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "[NaN, 20, 15, 0]"

[[test.results]]
value = "[NaN, 20, 15, 0]"

*/

RETURN vector::divide([10, -20, 30, 0], [0, -1, 2, -3]);

[NaN, 20, 15, 0]

vector::dot

The vector::dot function computes the dot product of two vectors, which is the sum of the products of the corresponding entries of the two sequences of numbers.

vector::dot(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "14"

*/

RETURN vector::dot([1, 2, 3], [1, 2, 3]);

-- 14

vector::magnitude

The vector::magnitude function computes the magnitude (or length) of a vector, providing a measure of the size of the vector in multi-dimensional space.

vector::magnitude(array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "8.54400374531753f"

*/

RETURN vector::magnitude([ 1, 2, 3, 3, 3, 4, 5 ]);

-- 8.54400374531753f

vector::multiply

The vector::multiply function performs element-wise multiplication of two vectors, where each element in the first vector is multiplied by the corresponding element in the second vector.

vector::multiply(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "[1, 4, 9]"

*/

RETURN vector::multiply([1, 2, 3], [1, 2, 3]);

-- [1, 4, 9]

vector::normalize

The vector::normalize function computes the normalization of a vector, transforming it to a unit vector (a vector of length 1) that maintains the original direction.

vector::normalize(array) -> array

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "[0.8f, 0.6f]"

*/

RETURN vector::normalize([ 4, 3 ]);

-- [0.8f, 0.6f]

vector::project

The vector::project function computes the projection of one vector onto another, providing a measure of the shadow of one vector on the other. The projection is obtained by multiplying the magnitude of the given vectors with the cosecant of the angle between the two vectors.

vector::project(array, $other: array) -> array

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "[1.6623376623376624f, 2.077922077922078f, 2.4935064935064934f]"

*/

RETURN vector::project([1, 2, 3], [4, 5, 6]);

-- [1.6623376623376624f, 2.077922077922078f, 2.4935064935064934f]

vector::scale

The vector::scale function multiplies each item in a vector by a number.

vector::scale(array, $other: number) -> array

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "[15, 5, 25, -15, 35, 10]"

*/

RETURN vector::scale([3, 1, 5, -3, 7, 2], 5);

-- [15,	5, 25, -15, 35, 10]

vector::subtract

The vector::subtract function performs element-wise subtraction between two vectors, where each element in the second vector is subtracted from the corresponding element in the first vector.

vector::subtract(array, $other: array) -> array

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "[1, 3, 5]"

*/

RETURN vector::subtract([4, 5, 6], [3, 2, 1]);

-- [1, 3, 5]

vector::distance::chebyshev

The vector::distance::chebyshev function computes the Chebyshev distance (also known as maximum value distance) between two vectors, which is the greatest of their differences along any coordinate dimension.

vector::distance::chebyshev(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "6f"

*/

RETURN vector::distance::chebyshev([2, 4, 5, 3, 8, 2], [3, 1, 5, -3, 7, 2]);

-- 6f

vector::distance::euclidean

The vector::distance::euclidean function computes the Euclidean distance between two vectors, providing a measure of the straight-line distance between two points in a multi-dimensional space.

vector::distance::euclidean(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "432.43496620879307f"

*/

RETURN vector::distance::euclidean([10, 50, 200], [400, 100, 20]);

-- 432.43496620879307f

vector::distance::hamming

The vector::distance::hamming function computes the Hamming distance between two vectors, measuring the minimum number of substitutions required to change one vector into the other, useful for comparing strings or codes.

vector::distance::hamming(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "1"

*/

RETURN vector::distance::hamming([1, 2, 2], [1, 2, 3]);

-- 1

vector::distance::knn

The vector::distance::knn function returns the distance computed during the query by the Knn operator (avoiding recomputation).

vector::distance::knn() -> number

The following example shows this function, and its output, when used in a SELECT statement:

/**[test]

[[test.results]]
value = "[{ id: pts:1, point: [1, 2, 3, 4] }]"

[[test.results]]
value = "[{ id: pts:2, point: [4, 5, 6, 7] }]"

[[test.results]]
value = "[{ id: pts:3, point: [8, 9, 10, 11] }]"

[[test.results]]
value = "[{ dist: 2f, id: pts:1 }, { dist: 4f, id: pts:2 }]"

*/
CREATE pts:1 SET point = [1,2,3,4];
CREATE pts:2 SET point = [4,5,6,7];
CREATE pts:3 SET point = [8,9,10,11];
SELECT id, vector::distance::knn() AS dist FROM pts
  WHERE point <|2,EUCLIDEAN|> [2,3,4,5];

[
			{
				id: pts:1,
				dist: 2f
			},
			{
				id: pts:2,
				dist: 4f
			}
]

vector::distance::manhattan

The vector::distance::manhattan function computes the Manhattan distance (also known as the L1 norm or Taxicab geometry) between two vectors, which is the sum of the absolute differences of their corresponding elements.

vector::distance::manhattan(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "13"

*/

RETURN vector::distance::manhattan([10, 20, 15, 10, 5], [12, 24, 18, 8, 7]);

-- 13

vector::distance::minkowski

The vector::distance::minkowski function computes the Minkowski distance between two vectors, a generalization of other distance metrics such as Euclidean and Manhattan when parameterised with different values of p.

vector::distance::minkowski(array, $other: array, $p_value: number) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "4.862944131094279f"

*/

RETURN vector::distance::minkowski([10, 20, 15, 10, 5], [12, 24, 18, 8, 7], 3);

-- 4.862944131094279f

vector::similarity::cosine

The vector::similarity::cosine function computes the Cosine similarity between two vectors, indicating the cosine of the angle between them, which is a measure of how closely two vectors are oriented to each other.

vector::similarity::cosine(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "0.15258215962441316f"

*/

RETURN vector::similarity::cosine([10, 50, 200], [400, 100, 20]);

-- 0.15258215962441316f

vector::similarity::jaccard

The vector::similarity::jaccard function computes the Jaccard similarity between two vectors, measuring the intersection divided by the union of the datasets represented by the vectors.

vector::similarity::jaccard(array, $other: array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "0.3333333333333333f"

*/

RETURN vector::similarity::jaccard([0,1,2,5,6], [0,2,3,4,5,7,9]);

-- 0.3333333333333333f

vector::similarity::pearson

The vector::similarity::pearson function Computes the Pearson correlation coefficient between two vectors, reflecting the degree of linear relationship between them.

vector::similarity::pearson(array, array) -> number

The following example shows this function, and its output, when used in a RETURN statement:

/**[test]

[[test.results]]
value = "0.9819805060619659f"

*/

RETURN vector::similarity::pearson([1,2,3], [1,5,7]);

-- 0.9819805060619659f